Very easy experiment: Just go to the front desk an thell them that you sadly seem to have lost your room card. 90% of the time they will just ask for your room number without requiring any kind of proof that it's actually your room.
Anecdotally, I was asked for ID each time my wife or I lost hotel room cards on 4 occasions (3 for me, once for my wife).
I believe they were 2 Courtyard Marriotts, 1 Residence Inn (Marriott), and a Sheraton (don't remember the hotel class).
EDIT: Grammar
In hindsight I might have tried asking for a different room number's key to see if she was paying attention and then quickly correct myself "No, just kidding, my room's 208 not 210. I just wanted to see if you'd give people any room key they ask for". Maybe that would've made them see the issue.
Instead, I took the easy route and made sure to never leave my netbook, passport, tickets, etc in the room (all the rest was replaceable and we were travelling light).
I would have probably done differently if I wasn't in a foreign country on a different continent and still getting used to the cultural uncanny valley of NYC being "almost, but not quite like Europe", so I opted for the safe choice of not being a bother to these obviously hard-working people.